As disclosed in Patent Literature 1, there is a power seat sliding device for vehicle seats having the following configuration: slide screws are disposed on, for example, upper rails with brackets therebetween; nut members screwed to the slide screws are disposed on, for example, lower rails; a motor is disposed between left and right sliders; rotation transmission shafts connected to the output shaft of the motor are connected to gear mechanisms disposed on the upper rails; the rotation driving force of the motor rotates the slide screws and changes the positions in which the nut members are screwed to the slide screws; and thus, the upper rails are moved back and forth relative to the lower rails along with the slide screws. Patent Literatures 2 and 3 disclose power seat sliding devices that each use flexible shafts (each consisting of an inner shaft in which steel wires are wound in multiple tiers and an outer tube covering the inner shaft; may be called flexible shafts, elastic torque cables, etc.) as rotation transmission shafts connecting between a motor and gear mechanisms and include means that absorbs the misalignment between the output shaft of the motor and the input shafts of the gear mechanisms to favorably transmit the rotational torque.